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A robot operating in a household makes observations of multiple objects as it moves around over the course of days or weeks. The objects may be moved by inhabitants, but not completely at random. The robot may be called upon later to retrieve objects and will need a long-term object-based memory in order to know how to find them. Existing work in semantic slam does not attempt to capture the dynamics of object movement. In this paper, we combine some aspects of classic techniques for data-association filtering with modern attention-based neural networks to construct object-based memory systems that operate on high-dimensional observations and hypotheses. We perform end-to-end learning on labeled observation trajectories to learn both the transition and observation models. We demonstrate the system's effectiveness in maintaining memory of dynamically changing objects in both simulated environment and real images, and demonstrate improvements over classical structured approaches as well as unstructured neural approaches. Additional information available at project website: https://yilundu.github.io/obm/.